The Vector v has a length of 15 and points at an angle of 30 degrees. The Vector u has a length of 17 and points at an angle of 55 degrees. What is u*v?

I know to get my answer I need to use this format |u|*|v|*cos(theta)
however I am stuck at setting up my vectors I only know <15,?> and <17,?>. Your help is appreciated greatly!

have you learned that any linear vector can be expressed as

(rcosØ , rsinØ) where r is the magnitude and Ø is the angle it makes with the horizontal.

so vector u = (15cos30°, 15sin30°)
= (15√3/2 , 15/2)
and
vector v = (17cos55, 17sin55)

u*v = 126.666600047 + 104.441885647)
or appr 231.1

check:
the angle between them would be 25°
231.1 = 15*17cosØ
cosØ = 0.906307787
and cos 25 = 906307..
my answer for u*v is correct

Thank you very much Reiny I was stumped on that but thanks to your assistance I was able to solve the problem. Thank you very much!

To solve this problem, we need to find the dot product of vectors u and v. The dot product of two vectors is calculated using the formula:

u*v = |u| * |v| * cos(theta)

where |u| and |v| represent the magnitudes (or lengths) of vectors u and v, and theta is the angle between them.

Given that the length of vector v is 15 and it points at an angle of 30 degrees, we can write vector v as:

v = <15*cos(30), 15*sin(30)>

Here, 15*cos(30) gives us the x-component of v, and 15*sin(30) gives us the y-component of v.

Similarly, for vector u, with a length of 17 and an angle of 55 degrees, we can write it as:

u = <17*cos(55), 17*sin(55)>

Now, we can proceed to find the dot product:

u*v = |u| * |v| * cos(theta)
= (17 * 15 * cos(theta))

To calculate the final result, we need to find the value of cos(theta). Since we have the angles in degrees, we use the cosine function with degree mode:

cos(theta) = cos(55 - 30)

Evaluating this expression, we get:

cos(theta) = cos(25)

Now, substitute this value back into the dot product formula:

u*v = (17 * 15 * cos(25))

Simplifying this expression will give you the final answer for u*v.